How is the depth of a CNN layer determined?
The 96 is the amount of filter maps (also: filter kernels). It is a fundamental of convolutional neural networks. The exact number is not arbritary, although there is no equation or exact rule of restricting the number.

If you have a CNN one single convolution operation would be pointless: since it used for the whole image information it can generalize, but only to specific (meaning: finite amount of) features. Easy example: if a 7x7 filter in the first layer concentrates on round shapes, it can not generalize on let's say red cubes at the same time.

Therefore you convolutional layers have several filter kernels, i.e. several weights where each is used for a convolution. The result of each of these convolutions is one filter map, i.e. the image information convolved by a kernel.

Typically you look at your filter kernels and your problem's domain to figure out what an appropriate number of filter kernels could be. You also have to keep in mind that too few kernels could possibly lose information and overfit to specific patterns, while too many kernels could possibly underfit. Especially when you have far more parameters (primarily the weights of your network) than training data your network will normally perform bad and you have to reduce its size.

The filter kernels should not be confused with batch size. The batch size is the amount of samples (here: images) you train in parallel. Each training step of your network does not only consist of feeding a single image, but feeding batch size number of images, usually combined with batch normalization steps between the layers. Hence, this has nothing to do the amount of filter kernels / convolutions of your network.